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Derive the expression for the capacitance of a parallel plate capacitor. And hence write the expression for the capacitance when a dielectric medium is inserted between its plates. |
Answer» Solution : Consider two parallel PLATES P and Q each of area A and separated by a distance d in AIR. Let plate P has surface CHARGE density `+sigma `and plate Q has surface charge density `- sigma ` . The electric field between the plates `E= (sigma)/(epsi_0) = ((q//A))/(epsi_0)` ` E = (q)/(A epsi_0)` But potential difference between plates, V = ED. Now capacitance, `C = q/V = (q)/(Ed) = (q)/((q)/(Aepsi_0) xx d)` `C = (epsi_0 A)/(d)` The capacitance of parallel plate capacitor when a DIELECTRIC medium is inserted between the plates is given by `C_m = (epsi_0 epsi_r A)/(d)` |
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